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Anti-D and B meson in nuclear medium at zero temperature

Anti-D and B meson in nuclear medium at zero temperature. Shigehiro YASUI (KEK). Recent progress in hadron physics -From hadrons to quark and gluon- @ Yonsei University, 18-22 Feb. 2013. 1. Introduction. Hadrons in nuclear medium are useful for study of ….

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Anti-D and B meson in nuclear medium at zero temperature

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  1. Anti-D and B meson in nuclear mediumat zero temperature Shigehiro YASUI (KEK) • Recent progress in hadron physics -From hadrons to quark and gluon- • @Yonsei University, 18-22 Feb. 2013

  2. 1. Introduction Hadrons in nuclear medium are useful for study of … (i) Interaction between hadron and nucleon Hyperon-nucleon interaction, hyperon-hyperon interaction Kbar-nucleon interaction (ii) Modification of properties of hadron π, ω, ρ, η(’) meson masses and decay widths in nuclear medium (iii) Change of medium caused by embedded hadron Shrink of radii of hypernuclei (“glue” effect by hyperon) Possible high density state in Kbar nuclei Fundamental questions in QCD: Color confinement, Spontaneous chiral symmetry breaking, …

  3. 1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry ΛQCD≈200 1500 [MeV] 4700 3 5 150 mass bottom charm up down strange Heavy Quark Symmetry Chiral Symmetry Change !! SU(3)L x SU(3)R SU(2NF)

  4. 1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry ΛQCD≈200 1500 [MeV] 4700 3 5 150 mass bottom charm up down strange • D, D (B, B) mesic nuclei • D, D (B, B)-nucleon interaction? • Modification of D, D (B, B) mesons • in nuclear matter (χSB)? • Change of nuclear matter? • How is QCD concerned? Heavy Quark Symmetry Chiral Symmetry Change !! SU(3)L x SU(3)R SU(2NF) D(cq) orD(cq)

  5. 1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry ΛQCD≈200 1500 [MeV] 4700 3 5 150 mass bottom charm up down strange • D, D (B, B) mesic nuclei • D, D (B, B)-nucleon interaction? • Modification of D, D (B, B) mesons • in nuclear matter (χSB)? • Change of nuclear matter? • How is QCD concerned? Heavy Quark Symmetry Chiral Symmetry Change !! SU(3)L x SU(3)R SU(2NF) D(cq) orD(cq)

  6. 5400 MeV “Particle” ≠ “Antiparticle” in nuclear matter Charge Conjugate 1870 MeV K D B 498 MeV “Particle” Including u, dquark - NO annihilation - NO absorption K D B “Antiparticle” Including u, dantiquark - Annihilation - Absorption

  7. 1. Introduction D and nucleon D and nucleon different D*+N (2947 MeV) D*+N (2947 MeV) D+N (2803 MeV) D+N (2803 MeV) Only DN and D*N channel Σc(2800) 1(??) π+Σc* (2658 MeV) C<0 C>0 Λc(2625) 0(3/2-) Λc(2595) 0(1/2-) π+Σc (2593 MeV) `Exoticchannel‘ `Baryonchannel‘ cqqqq cqqqq What is D/D-nucleon interaction ?

  8. 1. Introduction D and nucleon D and nucleon different D*+N (2947 MeV) D*+N (2947 MeV) D+N (2803 MeV) D+N (2803 MeV) Only DN and D*N channel Σc(2800) 1(??) π+Σc* (2658 MeV) C<0 C>0 Λc(2625) 0(3/2-) Λc(2595) 0(1/2-) π+Σc (2593 MeV) `Exoticchannel‘ `Baryonchannel‘ cqqqq cqqqq What is D/D-nucleon interaction ?

  9. 1. Introduction Strangeness, Charm, Bottom, ... Only NG boson (K) is important in dynamics, and vector meson (K*) is almost irrelevant… K* vector In cham/bottom, vector meson is also important! 400 MeV D* B* 140 MeV 45 MeV pseudo- scalar D B K 500 MeV 1870 MeV 5280 MeV sq cq bq q=u,d

  10. 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K B(*) D(*) N N N p, ω, ρ p, ω, ρ p, ω, ρ B(*) K D(*) N N N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force) Weinberg-Tomozawa interaction One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)

  11. 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K D* B* N N N p, ω, ρ p, ω, ρ p, ω, ρ K D B N N N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force) Weinberg-Tomozawa interaction One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)

  12. 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K D B N N N p, ω, ρ p, ω, ρ p, ω, ρ K D* B* N N N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force) Weinberg-Tomozawa interaction One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)

  13. 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K D* B* N N N p, ω, ρ p, ω, ρ p, ω, ρ K D* B* N N N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force) Weinberg-Tomozawa interaction One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)

  14. 1. Introduction Strangeness, Charm, Bottom, ... meson-nucleon interaction K D(*) B(*) N N N p, ω, ρ p, ω, ρ p, ω, ρ K D(*) B(*) N N N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force) Weinberg-Tomozawa interaction One-pion exchange potential (OPEP) SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012)

  15. 1. Introduction D and nucleon → New mechanism of DN interaction D*+N (2947 MeV) π D+N (2803 MeV) π Only DN and D*N channel S-wave D N “D-D* mixing” via pion exchange C<0 ・ Mass degeneracy for D and D* MD*-MD = 140 MeV ∝ 1/mc D* N D-wave ・π exchange (tensor force) S-D wave mixing (deuteron-like) D N S-wave → Some bound/resonant states `Exoticchannel‘ cqqqq SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) What is D/D-nucleon interaction ?

  16. 1. Introduction BN state From hadron-nucleon interaction to a variety of exotic nuclei 6263 MeV DN state B*N 2946 MeV 6217 MeV D*N BN B nuclei ? H dibaryon 2807 MeV 2255 MeV DN ΞN D nuclei ? ΛΛ Λ(1405) 2230MeV Hypernuclei 1433 MeV K(sq), Ξ(ssq), … KN K nuclei πΣ 1330 MeV

  17. 1. Introduction BN state From hadron-nucleon interaction to a variety of exotic nuclei 6263 MeV DN state B*N 2946 MeV 6217 MeV D*N BN B nuclei ? H dibaryon 2807 MeV 2255 MeV DN ΞN D nuclei ? ΛΛ Λ(1405) 2230MeV Hypernuclei 1433 MeV D(cq), B(bq) ?? KN K nuclei πΣ 1330 MeV

  18. 1. Introduction Quark-meson coupling model (Quark model) ・ K. Tsushima, D. -H. Lu, A. W. Thomas, K. Saito and R. H. Landau, Phys. Rev. C 59, 2824 (1999). ・ A. Sibirtsev, K. Tsushima and A. W. Thomas, Eur. Phys. J. A 6, 351 (1999). ・ K. Tsushima and F. C. Khanna, Phys. Lett. B 552, 138 (2003). QCD sum rule ・ F. Klingl, S. -s. Kim, S. H. Lee, P. Morath and W. Weise, Phys. Rev. Lett. 82, 3396 (1999. ・ Y. -H. Song, S. H. Lee and K. Morita, Phys. Rev. C 79, 014907 (2009). ・ K. Morita and S. H. Lee, Phys. Rev. C 85, 044917 (2012). ・ A. Hayashigaki, Phys. Lett. B 487, 96 (2000). ・ B. Friman, S. H. Lee and T. Song, Phys. Lett. B 548, 153 (2002). ・ T. Hilger, R. Thomas and B. Kampfer, Phys. Rev. C 79, 025202 (2009). ・ T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, 094054 (2010). ・ Z. -G. Wang and T. Huang, Phys. Rev. C 84, 048201 (2011). Hadron dynamics I (W-T interaction from SU(4) symmetry with breaking term) ・ A. Mishra, E. L. Bratkovskaya, J. Schaner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, 015202 (2004). ・ M. F. M. Lutz and C. L. Korpa, Phys. Lett. B 633, 43 (2006). ・ L. Tolos, A. Ramos and T. Mizutani, Phys. Rev. C 77, 015207 (2008). ・ A. Mishra and A. Mazumdar, Phys. Rev. C 79, 024908 (2009). ・ A. Kumar and A. Mishra, Phys. Rev. C 81, 065204 (2010). ・ C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, 015208 (2011). ・ A. Kumar and A. Mishra, Eur. Phys. J. A 47, 164 (2011). ・ C. Garcia-Recio, J. Nieves, L. L. Salcedo and L. Tolos, Phys. Rev. C 85, 025203 (2012). Hadron dynamics II (π exchange interaction) ・ S. Yasui, K. Sudoh, Phys. Rev. C87, 015202 (2013). ← Heavy Quark Symmetry + π exchange BN state From hadron-nucleon interaction to a variety of exotic nuclei 6263 MeV DN state B*N 2946 MeV 6217 MeV D*N BN B nuclei ? H dibaryon 2807 MeV 2255 MeV DN ΞN D nuclei ? ΛΛ Λ(1405) 2230MeV Hypernuclei 1433 MeV Dbar (B) meson – nucleon interaction must be very interesting !! KN K nuclei How is Dbar(B) meson bound in nuclear matter? πΣ Cf. Yamaguchi’s talk on few-body Dbar-nuclear systems in 19 1330 MeV

  19. 1. Introduction 2. Dbar and B mesonsbound in nuclear matter 3. “Strongcouplingproblem“ in heavymasslimit 4. Summary & perspectives

  20. 2.Dbar and B mesons in nuclear matter SY andSudoh, PRC87, 015202 (2013) Heavy meson Lagrangian(heavy quark symmetry & chiral symmetry) G. Burdman and J.F. Donoghue (1992) M.B. Wise (1992) T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.C. Lin and H.-L. Yu (1997) Multiplet field vector + pseudoscalar P*=D*bar P=Dbar Coupling const. from experimental value of deacy width of D*→Dπ ・ Mass degeneracy of Dbar and D*bar in heavy quark limit ・ Vertex strength: gπDD*=gπD*D* (spin symmetry) Self-energy of D in nuclear matter at order of two pion exchange Cf. Nuclear matter Kaiser, Fritsch, Weise, NPB697, 255 (2002); ibid. A750, 259 (2005) Fiorilla, Kaiser, Weise, Prog. Part. Nucl. Phys. 67, 317 (2012) Hypernuclear matter Kaiser, Weise, PRC71, 015203 (2005) Kaiser, PRC71, 068201 (2005) π Λc N N N N π in-medium nucleon propagator (Pauli exclusion principle) D* D D D D suppressed by 1/mD, 1/mD*, 1/mN D N D π π D* N D* N π π D N D DN scattering in vacuum D self-energy in matter

  21. 2.Dbar and B mesons in nuclear matter SY and Sudoh, PRC87, 015202 (2013) Self-energy of D in nuclear matter In-medium fermion propagator (kF: Fermi momentum) D D π D* D* π N Free Pauli exclusion in Fermi surface D D “particle” “hole” “particle” “hole”

  22. 2.Dbar and B mesons in nuclear matter SY and Sudoh, PRC87, 015202 (2013) Self-energy of D* in nuclear matter D* D* D* D* π D* D D* D π N D* D* D* D* “particle” “particle” “hole” “hole”

  23. 2.Dbar and B mesons in nuclear matter momentum cutoff : 1.27 × 0.7 GeV for Dbar 1.22 × 0.7 GeV for B Numerical results radius ratio × hyperon cutoff self-energy of D, B mesons in nuclear matter D -35 MeV Negative self-energies Bound in nuclear matter B -107 MeV Normal nuclear matter density

  24. 2.Dbar and B mesons in nuclear matter momentum cutoff : 1.27 × 0.7 GeV for Dbar 1.22 × 0.7 GeV for B Numerical results radius ratio × hyperon cutoff self-energy of D*, B* mesons in nuclear matter D* -150 – i160 MeV Negative self-energies (real), but large imaginary parts B* -200 – i120 MeV Bound but unstable in nuclear matter Normal nuclear matter density

  25. 2.Dbar and B mesons in nuclear matter Applications SY andSudoh, PRC87, 015202 (2013) ・ Atomic nuclei with D meson ・Isospin polarization V0=-35 MeV δ : density difference between p and n embedded in symmetric nuclearmatter Fine splittings (≈ten MeV) “Stable” distribution of isospin density Cf. “Isovector deformation” in Kbar nuclei Dote, Akaishi, Horiuchi, Yamazaki, PLB590, 51 (2004) → “Unstable” distribution of isospin density

  26. 2.Dbar and B mesons in nuclear matter Discussion on spin in heavy quark limit in QCD in vacuum Dbar (0-) : Qbar + q + qbarqq + gq + … ↑ “brown muck” - everything that is not the heavy quark (Isgur) ↓ degenerate D*bar (1-) : Qbar + q + qbarqq + gq + … ↑ ↑ Dbar and D*bar should be degenerate in vacuum. (Bottom is much better.)

  27. 2.Dbar and B mesons in nuclear matter Discussion on spin in heavy quark limit in QCD in medium Dbar (0-) : Qbar + q + qbarqq + gq + … + matter ↑ “in-medium brown muck” ↓ degenerate D*bar (1-) : Qbar + q + qbarqq + gq + … + matter ↑ ↑ Dbar and D*bar should be degenerate in vacuum. (Bottom is much better.)

  28. 2.Dbar and B mesons in nuclear matter Discussion on spin in heavy quark limit in QCD D π QCD-based result in medium -6 Q. Is there mass degeneracy in our formalism based on π exchange interaction? D* Dbar (0-) : Qbar + q + qbarqq + gq + … + matter π N ↑ “in-medium brown muck” D ↓ degenerate A. Yes. Dbar and D*bar in matter are degenerate in heavy mass limit (Δ∝mD*-mD→0). D* D* D*bar (1-) : Qbar + q + qbarqq + gq + … + matter π -4 -2 ↑ D* D ↑ π N D* D* Dbar and D*bar should be degenerate also in matter. (Bottom is much better.)

  29. 1. Introduction 2. Dbar and B mesonsbound in nuclear matter 3. “Strongcouplingproblem“ in heavymasslimit 4. Summary & perspectives

  30. 3. “Strong coupling problem” in heavy mass limit Heavy quark limit exists in matter as well as in vacuum. BUT always so? “Dbar, B meson” We critically discuss heavy mass limit in matter at zero temperature. Heavy “flavorerd” particle Φ (mass: MB→∞) “Nuclear matter” Fermi gas by fermionψ AssumptionsSY and Sudoh, arXiv.1301.6830 ・ Fundamental representation of SU(n) symmetry (isospin doublet for n=2) ・ Current-current interaction with λf・λB factor (λf/B: generator of SU(n) group) ・ Small coupling constant GB (so that perturbation can be applied.)

  31. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole 1st order (tree) 2nd order (one-loop)

  32. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole 1st order (tree) 2nd order (one-loop) ≈ GBMBλf・λB ≈ GB2MB Log(MB) λf・λB Logarithmic enhancement in loop diagram in heavy mass limit (MB→∞)

  33. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole

  34. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole Fermi surface MB: heavy boson mass, m: fermion mass

  35. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole MB = ∞ case denominator = 0 for Singularity on Fermi surface Fermi surface MB: heavy boson mass, m: fermion mass

  36. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole MB = finite case denominator = 0 for No singularity on Fermi surface Fermi surface MB: heavy boson mass, m: fermion mass

  37. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole MB = finite MB= ∞ Log MB Nosingularity Singularity Logarithmic Fermi surface MB: heavy boson mass, m: fermion mass

  38. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole

  39. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle ↑ ↑ ↑ ↑ + + … = + ↑ ↑ ↑ ↑ hole

  40. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle ↑ ↑ ↑ ↑ ↑ + + … = + ↑ ↑ ↑ ↑ ↑ ↑ ↑ hole 1. Spin non-flip in intermediate state → Logarithmic singularity at Fermi surface is canceled.

  41. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle ↑ ↑ ↑ ↑ ↓ + + … = + ↑ ↓ ↑ ↑ ↓ ↑ ↓ hole 2. Spin flip in intermediate state

  42. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle ↑ ↑ ↑ ↑ ↓ + + … = + ↑ ↓ ↑ ↑ ↓ ↑ ↓ hole 2. Spin flip in intermediate state → Logarithmic singularity at Fermi surface is NOT canceled. Cf. “Kondo problem” by J. Kondo (1964); log|q-kF| for q→kF, MB=∞.

  43. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole 1st order (tree) 2nd order (one-loop) ≈ GBMBλf・λB ≈ GB2MB Log(MB) λf・λB Logarithmic enhancement in loop diagram in heavy mass limit (MB→∞)

  44. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy boson Φ Heavy boson Φ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Φ: Dbar (B) meson Heavy boson Φ with mass MB particle + + … = + hole 1st order (tree) 2nd order (one-loop) ≈ GBMBλf・λB ≈ GB2MB Log(MB) λf・λB “Strong coupling problem” inλf・λB-dependent interaction in MB→∞ (isospin)

  45. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy fermionΨ Heavy fermionΨ in matter Fermionψ (matter) Heavy fermionΨ with mass MF

  46. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy fermionΨ Heavy fermionΨ in matter Fermionψ (matter) Heavy fermionΨ with mass MF particle + + … = + hole 1st order (tree) 2nd order (one-loop) ≈ GFλf・λF ≈ GF2Log(MF) λf・λF “Strong coupling problem” inλf・λF-dependent interaction in MF→∞

  47. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy fermionΨ Heavy fermionΨ in matter Fermionψ (matter) Nuclear matter with isospin SU(2) ψ: nucleon Ψ: Λc baryon ??? Not applicable, because Λc is NOT doublet in SU(2) !! Heavy fermionΨ with mass MF particle + + … = + hole 1st order (tree) 2nd order (one-loop) ≈ GFλf・λF ≈ GF2Log(MF) λf・λF “Strong coupling problem” inλf・λF-dependent interaction in MF→∞

  48. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy fermionΨ Heavy fermionΨ in matter Fermionψ (matter) Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3crepresentation of color SU(3) Heavy fermionΨ with mass MF particle + + … = + hole 1st order (tree) 2nd order (one-loop) ≈ GFλf・λF ≈ GF2Log(MF) λf・λF “Strong coupling problem” inλf・λF-dependent interaction in MF→∞ (color)

  49. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy fermionΨ Heavy fermionΨ in matter Fermionψ (matter) Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3crepresentation of color SU(3) Heavy fermionΨ with mass MF particle R R R R R + + … R R = + R R R R R hole “color non-flip” 1st order (tree) 2nd order (one-loop) ≈ GFλf・λF ≈ GF2Log(MF) λf・λF “Strong coupling problem” inλf・λF-dependent interaction in MF→∞ (color)

  50. 3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv.1301.6830 Scattering amplitude for fermionψ and heavy fermionΨ Heavy fermionΨ in matter Fermionψ (matter) Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3crepresentation of color SU(3) Heavy fermionΨ with mass MF particle R R R R B + + … B B = + R R R R B hole “color flip” 1st order (tree) 2nd order (one-loop) ≈ GFλf・λF ≈ GF2Log(MF) λf・λF “Strong coupling problem” inλf・λF-dependent interaction in MF→∞ (color)

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